Question

Two brands of car​ batteries, both carrying​ 6-year warranties, were sampled and tested under controlled conditions. Five of each brand failed after the number of months shown. Calculate ​a) both sample means and ​b) both sample standard deviations. Decide ​c) which brand battery lasts longer and ​d) which brand has the more consistent lifetime. Brand​ A: 68​, 69​, 76​, 76​, 73 Brand​ B: 61​, 69​, 68​, 67​, 61

What are the sample​ means?A B

What are the sample standard​ deviations? SA SB

Which brand battery apparently lasts​ longer?BRAND A OR B

Which brand battery has the more consistent​ lifetime?BRAND A OR B

Answer 1

The sample size is n = 5 . The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	A	A2
	68	4624
	69	4761
	76	5776
	76	5776
	73	5329
Sum =	362	26266

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

The sample size is n = 5. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	B	B2
	61	3721
	69	4761
	68	4624
	67	4489
	61	3721
Sum =	326	21316

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

What are the sample​ means?

A : 72.4

B : 65.2

What are the sample standard​ deviations?

SA : 3.782

SB : 3.899

Which brand battery apparently lasts​ longer?

BRAND A ( high mean )

Which brand battery has the more consistent​ lifetime?

BRAND B ( high standard deviation )